Question

Loan amortization schedule Personal Finance Problem Joan Messineo borrowed $41,000 at a 4% annual rate of interest to be repaid over 3 years. The loan is amortized into three equal, annual, end-of-year payments. a. Calculate the annual, end-of-year loan payment. b. Prepare a loan amortization schedule showing the interest and principal breakdown of each of the three loan payments. c. Explain why the interest portion of each payment declines with the passage of time. a. The amount of the equal, annual, end-of-year loan payment is $ (Round to the nearest cent.) b. Prepare a loan amortization schedule showing the interest and principal breakdown of each of the three loan payments. Many financial calculators have an amortization function which makes this process easy. Once the payment is determined in step a above, you can use the AMORT function to calculate the interest paid, principal paid and ending loan balance for each payment period. You should consult your calculator instructions for specific details pertaining to your calculator. What is the account balance at the beginning of year 1? (Round to the nearest cent.)

Answer 1

The annual, end-of-year loan payment is $13,616.02. The interest portion of each payment declines with time. The account balance at the beginning of year 1 is $41,000.

To calculate the annual, end-of-year loan payment for a loan amortized into three equal, annual, end-of-year payments, we can use the formula:

R = PV / ((1 - (1 + i)^(-n)) / i)

In this case, the principal amount (PV) is $41,000, the annual interest rate (i) is 4%, and the loan term (n) is 3 years.

Substituting the values into the formula:

R = $41,000 / ((1 - (1 + 0.04)^(-3)) / 0.04)

Solving this equation, we find that the annual, end-of-year loan payment is $13,616.02 (rounded to the nearest cent).

The loan amortization schedule will show the interest and principal breakdown of each of the three loan payments. The interest portion of each payment will decline with the passage of time because the outstanding principal balance decreases over time as the loan is repaid.

At the beginning of year 1, the account balance is the initial principal amount, which is $41,000.